You should be getting this tip when opening the game of luck for the first time:
The Game of Luck is a fun way to win huge amounts of gold and virtually all game cards! To play the Game of Luck now select the deck. You can do it as much as you want, but be aware that every new play will cost you more and more gold. However the price will start to drop slowly and in 6 hours it will be reset completely. A word to the wise: the more it costs, the greater is the chance of getting a great reward!

After every play (click) the chances will increase and get better up to a specific level. At this level they stay constant.
After 6 hours from the last play, the game is reset.

Thanks ... but how much gold does it cost until you reach the best chance? It is important to know this information in order to decide how much to save up before playing the Game of Luck. For example does it take 1000 gold (100 tries) and then the odds are best, or does it take 10,000 gold? If you receive a Mythic card does the percentage decrease again, or does it stay elevated?

The game of luck is played in levels. Every level doubles the cost to play.
The first level is 10 gold. The next level is twice as much - 20. And so on ... up to level 11 which is the top level.
Then the gold price is constant until the game is reset.
Hope this helps!